In upstream layer of the industry, there is a single supplier, Supplier 1, whose marginal cost of production is 1. The downstream industry is competitive and buys inputs from the upstream supplier at the cost of k. Downstream industry also hires workers at a competitive wage of w=$2. The firms in downstream produce a final good using the production function =^1/2^1/2, where K and W are the amounts of inputs purchased from Supplier 1 and labor market, respectively. The inverse demand faced by downstream industry is P=20-3Q.

1. Find equilibrium prices k and P, quantities K, W, and Q, and the profits in the supply chain.
2. Compute prices, output, and profits if downstream and upstream firms would vertically integrate.
3. Please provide solution with answers I am stuck and looking for help on the solution, please don't use chat gbt